Question

What are the types of variations ? Explain all

Answer 1

Variations are classified either as continuous, or quantitative (smoothly grading between two extremes, with the majority of individuals at the centre, as height varies in human populations); or as discontinuous, or qualitative (composed of well-defined classes, as blood groups vary in humans).

Answer 2

Answer:

The types of variations are ↴

✑ Inverse variation

✑ direct variation

Step-by-step explanation:

DIRECT VARIATION ↴

Direct Variation is said to be the relationship between two variables in which one is a constant multiple of the other. For example, when one variable changes the other, then they are said to be in proportion. If b is directly proportional to a the equation is of the form b = ka (where k is a constant). Two variables are said to be in direct variation when the variables are related in such a way that the ratio of their values always remains the same. Direct variation is expressed in various mathematical forms. In equation form, y and x vary directly since the ratio of y to x never changes.

Solved Example⤵️

✎ The quantity of wooden box made is directly proportional to the number of wooden blocks. The number of wooden blocks needed for 30 boxes is 120. How much wooden blocks are needed for a box?

Solution ↴

In the given problem,

Number of wooden blocks needed for 30 boxes = y = 120

Number of boxes = x = 30

Number of wooden blocks needed for a box = k

The direct variation formula is,

y = k * x

120 = k * 30

k = 120/30

k = 4

Number of wooden blocks needed for a box = 4

INVERSE VARIATION ↴

Unlike the direct variation, where one quantity varies directly as per changes in another quantity, in case of inverse variation, the first quantity varies inversely as per another quantity. Hence, it is also called the inverse proportion.

Inverse Variation Word Problems⤵️

✎ Illustration 1: 9 pipes are required to fill a tank in 4 hours. How long will it take if 12 pipes of the same type are used?

Solution: Let, the desired time to fill the tank be x minutes. We know that as the number of pipes increases, the time taken to fill the tank will decrease. Hence, this is a case of inverse variation. In other words, the number of pipes is inversely proportional to the time taken. Thus,

\frac{x_1}{x_2}~=~\frac{y_2}{y_1}

\Rightarrow~\frac{9}{x}~=~\frac{12}{4}

x ➪ 3 hours